Phase Splitting for Periodic Lie Systems

Details Phase Splitting for Periodic Lie Systems Phase Splitting for Periodic Lie Systems

2009-10-14

arxiv.org/abs/0910.2575v2

J. Phys. A: Math. Theor. 43, 205208 (2010).

Physics

Mathematical Physics

(v1) 15 pages. (v2) 16 pages. Some typos corrected. References and further comments added. Final version to appear in J. Phys.

Scientific paper

10.1088/1751-8113/43/20/205208

In the context of the Floquet theory, using a variation of parameter argument, we show that the logarithm of the monodromy of a real periodic Lie system with appropriate properties admits a splitting into two parts, called dynamic and geometric phases. The dynamic phase is intrinsic and linked to the Hamiltonian of a periodic linear Euler system on the co-algebra. The geometric phase is represented as a surface integral of the symplectic form of a co-adjoint orbit.

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